-8w(w-6)=32

Solution for -8w(w-6)=32 equation:

Simplifying
-8w(w + -6) = 32

Reorder the terms:
-8w(-6 + w) = 32
(-6 * -8w + w * -8w) = 32
(48w + -8w2) = 32

Solving
48w + -8w2 = 32

Solving for variable 'w'.

Reorder the terms:
-32 + 48w + -8w2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 48w + -8w2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + 6w + -1w2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + 6w + -1w2)' equal to zero and attempt to solve:

Simplifying
-4 + 6w + -1w2 = 0

Solving
-4 + 6w + -1w2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -6w + w2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6w + -4 + w2 = 0 + -4

Reorder the terms:
4 + -4 + -6w + w2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6w + w2 = 0 + -4
-6w + w2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6w + w2 = -4

The w term is -6w.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6w + 9 + w2 = -4 + 9

Reorder the terms:
9 + -6w + w2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6w + w2 = 5

Factor a perfect square on the left side:
(w + -3)(w + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(w + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1
w + -3 = 2.236067978

Simplifying
w + -3 = 2.236067978

Reorder the terms:
-3 + w = 2.236067978

Solving
-3 + w = 2.236067978

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + w = 2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + w = 2.236067978 + 3
w = 2.236067978 + 3

Combine like terms: 2.236067978 + 3 = 5.236067978
w = 5.236067978

Simplifying
w = 5.236067978

Subproblem 2
w + -3 = -2.236067978

Simplifying
w + -3 = -2.236067978

Reorder the terms:
-3 + w = -2.236067978

Solving
-3 + w = -2.236067978

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + w = -2.236067978 + 3

Combine like terms: -3 + 3 = 0
0 + w = -2.236067978 + 3
w = -2.236067978 + 3

Combine like terms: -2.236067978 + 3 = 0.763932022
w = 0.763932022

Simplifying
w = 0.763932022

Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {5.236067978, 0.763932022}
Solution
w = {5.236067978, 0.763932022}